What is a dex?

Sep 25, 2014

The term “dex” comes up rather frequently in astronomy discussions but is
rarely defined in textbooks. The idea of a dex is straightforward—a dex
is simply an order of magnitude. More formally, a difference of dex
is a change by a factor of . (Although the dex is almost always
used in relation to some other quantity, it can in principle be used to
represent a unitless number. Thus the number can be written
dex.)

We use the terms “order of magnitude” and “factor of ” all the time,
though, so why use the term dex? The reason is that it comes in handy when
talking about fractions of an order of magnitude. It’s particularly useful
when talking about metallicity. Metallicity is measured logarithmically
relative to the abundance of metals in the Sun, and accordingly it must be
unitless.

As an example, let’s take a look at Fischer & Valenti (2005). In this
paper the authors present a correlation between the metallicity of stars and
the probability that the star hosts a planet—stars with higher
metallicities are more likely to host a planet. This result is shown in
figure 5:

Fischer & Valenti (2005)

We can see that the sample of stars spans a range of [Fe/H] from -0.5 to
0.5, which is one order of magnitude, or one dex. Although it was just as
easy to say order of magnitude as it was to say dex in that case, suppose we
asked how wide the bins in this histogram were. There are ten bins spanning
an order of magnitude, so the width of each bin is a factor of . This is clumsy, so instead we simply say that each bin has
a width of 0.1 dex.

A dex is completely equivalent to a “bel” or “decade” which occasionally
come up in engineering and physics. The bel is much more widely known with
its deci- prefix as the “decibel.” A decibel is therefore equal to 0.1 dex.

As a historical footnote, the term “dex” was coined by the astronomer C. W.
Allen of Allen’s Astrophysical Quantities fame. He originally proposed
the term in the 1948 meeting of the International Astronomical Union in
Zurich and in 1951 published a short note advocating its use. The
physicist J. B. S. Haldane took up the cause of the dex in 1960 with a short
note published in Nature advocating its wider use outside of astronomy
and physics, particularly in biology. It seems, however, that the
biologists and other scientists were not as keen on the dex because it
remains limited to the jargon of astronomy.